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Second order effects, that rational types fail to grasp

Gamedevs can make better games with AI! Yet the creatives don't get into gamedev if they didn't have to spend any effort to make their art

Mathematicians can advance mathematics with AI! Yet mathematicians don't get into mathematics because they want to "advance" mathematics

Teachers can teach better with AI, writers can write better with AI.. Can they?

Can't you people understand romance and the beauty of the human endeavor

> It's the bedrock of all other science. The goal is to find solutions and to advance the field…

That may be true but that may not be the feature that attracts people to the field.

> As we solve lower level problems, we can unlock real world math solutions.

That is an argument often made for funding mathematics research. But again it may not be the thing that attracted people to the field.

Note I don’t share all the doom and gloom of some folks in the math community but it is a valid point that people who might otherwise have gone into the field may choose not to anymore.

Also, math research has typically focused a large amount of energy abstracting and generalizing results. Your suggestion about solving real problems usually moves in the other direction. If the powers that be with all the money decide AI can solve all the real problems that exist (rightly or wrongly) then mathematics research community will have a problem.

I think "fun" and "meaningless" are important parts of math. There is applied math for sole utility. Other math is just random search that may or may not be useful in long term. But later people/AI will find important use cases from these short-term "meaningless" researches.

Let me help you by breaking down your point.

> The goal is to find solutions

> and to advance the field

Nobody seems to be disputing LLMs help with the former, but some are concerned that the latter is jeopardized by having aliens do our homework.

It's both. Some math has applications. Some math doesn't. Many mathematicians are interested in mathematical beauty, in solving problems, and playing with puzzles.

None of the results from October 6, as far as I know, have direct real-world applications today. We can't go build a better thing, or make a faster thing, etc. I might be missing something (I'm not an expert in any of the fields). I don't think most folks would have a problem with solving a bottleneck problem that let us flux a capacitor at 2x efficiency, or whatever.

I also think this is hard for a lot of folks who are in fields that heavily apply math to come to terms with. I do not think that programming and practicing mathematics are the same: many (most?) mathematicians are closer to a composer than a programmer: all three are making things, but there is much more emphasis on elegance and cleverness in mathematics than in programming.

But again, it's not binary, and a lot of the discussion does try to take a black-or-white view of it. It's tradeoffs all the way down.

For what it's worth, I think this quote from the article sums up my position best:

"To me, someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution. I would give that person substantial credit even if they supplied no new ingredient in the original proof. Choosing worthwhile problems may end up mattering more than producing proofs."

> It's the bedrock of all other science.

no, its just a language. physics constrains 1+1. "one plus one equals two" is difficult to transform

> understands it thoroughly, and uses it to develop interesting further questions or directions

He phrases it like these criteria are requirements, but they really aren't for every problem. They make sense for those theoretical problems whose solutions' main values lie in their understandability and further development, but not every problem is like that. Some problems' solutions are just revolutionary on their own even if you contribute or understand absolutely nothing else. AI technology itself is an example of this!

To give a trivial hypothetical counterexample: if you came up with a solution for the traveling salesman problem that is both empirically sufficiently faster than the state of the art, that is an immense contribution and you absolutely deserve the credit for it regardless of whether you or anyone else understands how/why it works. It could literally even produce wrong results 50% of the time and still revolutionize humanity if it's efficient enough when it's correct. Denying them credit because they didn't understand the algorithm would be ludicrous - the results stand & speak for themselves.

Statisticians, traditional-AI researchers, etc. had to learn this the hard way when (basically black-box) neural nets became so good that their otherwise-elegant & explainable classical algorithms just stopped being able to compete in more and more applications, and got left behind. Are mathematicians looking to repeat that history?

This echoes SICP's admonition that "Programs must be written for people to read, and only incidentally for machines to execute."

Which is absurd on it's face for most day to day programmers, but a critical distinction for theoretical computer scientists.

The fact that this wouldn't have been considered a contribution before, or that this is a novel idea, suggests that there was something wrong with mathematics culture all along. I'm glad they're figuring it out now, but it seems "too little too late" after decades of devaluing all expository and exploratory work other than writing difficult proofs.

Understanding is what takes the time. Understanding what someone else wrote is harder than understanding something you wrote.

The time saved using AI comes from reducing understanding.

> Mathematics has become a field where results themselves matter less

Results are the only things that truly matter. Everything else is a position advocating for someone’s quality of life.

> writing code can sometimes be delegated to AI, and is arguably less important than understanding what the customer really wants from this software.

It’s still early days and the LLM can already ask the customer what they want directly.

I feel like the hyper-competitiveness of academia generally is the elephant in the room.

The disaster for a problem-solution-oriented mathematician isn't that once problem-solution is easy they'll just switch to theory-explanation and machinery-building. It is that they will have to compete (and won't be able to compete) with students and post-docs who've been doing theory-explanation and machinery-building for their entire career - and there are lots of these 'cause academic pipeline produces more people who can fill a job than jobs in every imaginable category and subcategory.

One of the best comments I read this month and in October

> Mathematics has become a field where results themselves matter less

"Results" in mathematics has always been the proof. (Preferably a beautiful and succinct one.)

Math is supposed to expose the workings of the epistemological foundations of the universe. The result itself (number or formula or whatever) is absolutely irrelevant to math.

(It may be important to physics, chemistry or engineering, but it isn't to math.)

fewer mathematicians means fewer problems to solve. All problems have human origin, right? Can AI create a problem on its own and what would be the point? Closer to can god create a stone he can't lift.

The quote reads to me like “as long as you can analyze the solution after the machine solves it and make it suggest new ideas based on that, you’re almost the same as a discoverer yourself.” I’m deliberately avoiding “mathematician” here because I think Tao probably didn’t intend to take it that far. But, for many people that difference will be indistinguishable, especially because there will very likely be “math bros” just like “ai bros” and “crypto bros” before them who want to pretend they’re mathematicians just as we see people pretending to be engineers and financial experts based on how fast they got on the hype train.

I’m no mathematician, though I do have an undergrad degree in math, and unless I had a graduate degree or made substantial contributions at that level, I would never consider myself anything but a “student of mathematics,” and that too not just because I have a degree in the subject, but because I still have a great interest in certain branches of math and I keep learning in my spare time from books or from adjacent applied fields I continue to formally study. As a kid, I grew up hating math but I became interested in it later in life because of coding, computer science and formal logic, pushing myself a lot through my college years to get some foundational understanding of the subject at a deeper level than the general population, just to get my foot in the door, so to speak.

Even if I’m an outsider from the circle of mathematicians, this whole AI takeover of mathematics leaves such a bad taste in my mouth because I’ve long felt that math was one of those things that everyone could agree is a useful and beneficial thing for humanity in general, and it was one of the least divisive fields, where people from different parts of world, from different stations in life could participate, and very few points, especially today, caused any controversy (unlike just about every other subject). It feels like a great loss for humanity to lose a brunt of our engagement with it to the machines, like a whole wing of a gigantic library starting to be closed off from us indefinitely because some people decided that we don’t _need_ to access it anymore, except on an even grander scale possibly than my imaginary library metaphor.

Sure, but given the approximate tens of millions of dollars in API costs of solving these major math problems currently, we will also have to acknowledge that getting credit for major mathematical contributions is likely now to be far less about meritocracy and far more about access to capital to kickstart the original proof.

Less capable (but good enough) mathematicians with more capital will have a huge advantage over great mathematicians who are broke.

I'm not a mathematician, but that situation rubs everyone (except those with the most capital) the wrong way.

It's still confusing to call that a "change". Apart from the way the media covers the topic, I've never known mathematics to be about proofs.

I'm so glad that sanity ulitmately won in his mind.

>> where writing code can sometimes be delegated to AI, and is arguably less important than understanding what the customer really wants from this software.

This statement is a monstrosity, and the reason why real software engineers know vibe coding will fail. It is fundamental misunderstanding of thinking that that the intellectual work consists of knowing what you want, and coding is merely the mechanical labor of making it happen.

The coding is the intellectual work!

Its where the actual problems are discovered, where the difficult decisions are made, where vague ideas become precise, and where solutions are invented. There is not such thing as a fully formed solution waiting to be translated into code. :-)

Again just the modern variation of the idea guy who goes around saying I have a genius idea for a new startup...I just need some Developers to implement it ....

>and don't dream big enough

People have been dreaming running PS5 games on PC for a long time. Just when AI starting to become capable of doing that, Anthropic shut it down.

Yeah you can dream, but only what we allow.

To a first approximation I agree that it’s similar to industrialization. However there’s a key factor which distinguishes this case, and which makes the analogy less than perfect: there isn’t a profit motive in mathematics, so there was no push for this development from inside the field. Instead, the industrialization was entirely exogenous, from companies which do in fact have that profit motive and view math as a means to achieve it.

There might be a “proof motive” in math which one could argue will drive the full automation of theorem proving. But we must recognize that profit is more universally valuable (i.e. it has value outside the industry in which it was created), whereas proofs are only valuable inside the math community (at least the pure math proofs the labs have been publishing thus far).

This is really well put, I totally agree with you.

There’s an immediate resistance towards change rather than embracing it and finding opportunities to improve and work with it.

> My recent take on AI is that people haven't adapted to the new huge potential of the tool, and don't dream big enough (yet).

I guess you can dream big enough only if you have access to the really interesting models. The 20$ subscription won't get you there, and the 100$ one is already out of reach for so many people.

That is a great example, car engines (and derivatives) did create tremendous economical value but are in the process of making our planet unhabitable.

Maybe we should listen to people that care about negative externalities more often, and actually mitigate them.

Two possible walls for advancing math with AI: first, it could be that the kind of problems that AI solves are the ones that don't open new avenues to concepts and ideas, and second, problems complexity is usually not linear, and the new and interesting problems to solve could be at a level of complexity beyond what AI can currently solve. Perhaps mathematicians could work to find ways to help AI cope with those walls.

How you get somewhere is important and tools change how you get there.

You can drive 1000 miles and arrive at the destination on the highway quickly.

Or you can take the slow road and walk. You discover unrelated things, make new relationships, see the scenery, listen and smell what is around you and have time to contemplate things which may or not be related.

This particular tool economy robs us of all these things in the rush to the destination.

I'd sacrifice "progress" a little for some of the better bits of humanity.

Yes, this. Unless there is a true singularity where no more questions are ever asked, there will be definition be infinitely many problems to solve, and most of them we have not even glimpsed yet.

Singularity? Probably not.

Tech bro dictatorship? Unfortunately a bit more likely.

None of the above? Then we have a small shot at a great future.

Having a machine that solves hard problems must be a good thing.

Because the other option is that AI does what you say. And if you think about it (and you are a mathematitian and not an engineer) it means that AI is able to read our minds and know our desires. And at that point who cares about existence anymore?

Ive noticed that too, I don’t know why people talk like we need to figure this out right now

Like we can even know what the future of math is this early

It’s not like you can just declare that up front, it’s something that happens naturally when people spend time using the tools

Just because they could, doesn't mean anyone would bother having the AI agents do so.

Because if you assume there is going to be an AI-god that can do everything better than us, there's nothing to really do. Like really, what do you want these people to write? "Well, math for humans is over as well as all intellectual activity, better just jerk off watching AI-generated hentai all day until I die"

Not only are the proofs long and unintelligent, but they don't cite previous work.

In fact, they completely disregard all standards of mathematical dissemination. They just post a bunch of 100+ page papers online and call it the day.

A real mathematician polishes and polishes for months until it is understandable by the community. Then they communicate the results to a journal where there are editors and peer reviewers who come with detailed feedback which is then implemented. And just then it is ready to publish.

> The main practical complaint is "what do I do now", especially from PhD students who just lost their thesis topic. They sound like the Uber drivers fighting Waymo.

I wish mathematicians would just focus on this. This really is the problem, at the end of the day.

Having models get better at writing elegant proofs and explaining their results will not solve this problem - it will only make it worse, if anything.

We are all sympathetic to this. I, personally, am much less sympathetic to the absurd notion that it is "bad" that this new technology can solve important open mathematical problems at all, that we should stop trying to solve them, that things like the Mathathon are dangerous and needs to be shut down, that ugly proofs are the real problem here, so much so that you wish the open question weren't resolved at all, and so on. So silly.

But being pissed off that people are going to be out of work is something I agree 100% on. Hopefully, much like the internet, there's a way to make the whole thing a net benefit for society.

Technology has changed and extended the craft, but everything about developing applications and communicating results remains.

He did attach his name to it by posting it. I'd imagine if he disagreed strongly he wouldn't do that, or he would at least add a footnote.

What you could argue though is that he is muddying the waters with all these guest posts on a domain that is as personal as it gets. I appreciate he's trying to be the 'Carlos Santana of mathematics' by sharing the spotlight but it might be good to highlight the distance a bit more, for instance by adding his own views.

None of the OpenAI papers published with a Lean formalization have been retracted.

But in a human way? I don't think so. The 700+ solutions that were put out by openAI are in no way accepted as solved until humans say so. It's kind of like saying SC2 was solved when Alpha beat the best players. The professional community just went on playing much the same. Math should do the same. Just with better tools

> The point is that AI will be able to advance on any problem better than any human.

Define "better".

I don’t think we know whether or not that’s true yet. Imagine a problem which requires a paradigm shift or new novel techniques to solve. There is no proof (yet) that an AI could create one.

Did any ai made any new interesting question or conjecture?

ANY problem?

But the question is whether the AI will itself be able to decide on which problem to advance, and do it in an ethical and aligned way with humanity. And that if it does, its significance will be understood by humans.

Otherwise we're just creating a black box, easily manipulated by their owners, who would be ruling over human lives. That's not what people want

The thing about much human progress on various problems is that human mathematicians formulate a human comprehensible machinery for the purposes of solving a given problem and then that machinery naturally suggests (to humans) further questions which then give rise to more machinery - And, in a sense, the value is ultimately the machinery, which has tended in the past to be relevant to physics, computer science, logistics, sociology and philosophy.

When AI writes proof no human can understand, it doesn't advance mathematics this way. Maybe AIs can understand their own proofs - meaning not just verify them but extract a machinery/broader-perspective (but I wouldn't count on it). But even machinery an AI isn't necessarily useful for humanity/society.

But how do you know which problems are worth making progress on? Traditionally, you'd find those by working on solving previous problems.

> The point is that AI will be able to advance on any problem better than any human.

If that was true it would of course be significant.

If you had no morals, 2 trillion dollars to spend, ability to commit intellectual property theft without consequences, and most of the smartest people in the world actively working to advance your cause... ...you really think you couldn't compete with the clankers?

> I think the model helps mathematicians more than it hurts them

I would agree with you if these models were available to mathematicians, and OpenAI wasn't effectively competing with them by spending millions of dollars in compute to rush out solutions.

Better at investigating the idea that one could conceive of elements in the different commensurability classes of compact arithmetic hyperbolic three-manifolds indexed by non-split quaternion algebras {D/F} as forming some type of geometric Kolyvagin system (“Heegner points”) associated to {K_3(F)}, which one could yoke together by some unknown integral arithmetic version of the Jacquet–Langlands correspondence?

IMO, this captures well the essense of AI: it's an alien swarm intelligence that solves problems with brute force and pattern matching. For comparison, we prefer simple and elegant solutions, partly because our time and attention scope is very limited, but mainly because it rhymes with our nature.

Academia is almost entirely a patronage network. It was never about results.

https://archive.org/details/colossus-the-forbin-project-1970...

here is the direct link of the video which starts at 1800 seconds.

Offtopic: Fun fact but aside from archive.org there is also a way to have a link which links to any direct video at any time.

Someone made a good HN article about it that I vaguely remembered[0]

[0]: https://www.autodidacts.io/how-to-deeplink-to-specific-part-...

This is another 15 min phase like “prompt engineering”. Soon it’s going to be just a CEO and an LLM.

They solved a millennium prize problem… they disproved the exponential time hypothesis. Are those low hanging fruits?

> But those are just low hanging fruits, i.e problems that humans were too lazy to deal with.

Some of these problems have had mathematicians dedicating their careers towards getting closer to a solution. Your comment reads like wishful thinking.

It's amazing to still see posts like this in late 2026. I suggest you recalibrate your ideas on what both AI and human intelligence is and can do. My take: both are trained systems. Both are as "statistical" as the other. Any idea that "because statistics" means that humans are different or better is bogus. Both can do things based on their training data. You are totally correct that a human has access to training data that AI doesn't (the smell of new mown hay, for example, or the fear of being crushed by the garbage compactor room in Star Wars). But there's no "humans have more training data therefore better" argument to be made about fields like mathematics. In fact the opposite argument works quite well: AI can have all mathematics ever invented in its training data, something that's pretty hard to achieve as a human.

I won't even start on "AI is unconscious"...

I think Sutton agrees [1].

[1] https://youtu.be/ThFq87Rp21s?is=xvgU-cKCpK0KwG_M

People are allowed to process their anxieties. And processing takes time. That said publicly doing it on the great modern internet attention/noise factory complicates the story.

I don't think it was a particularly well-reasoned essay (I thought the classification of finite simple groups is almost evidence for the opposite of what he says), but at the same time I don't think you understood his point.

If we have a theorem proving machine, then we can use it to prove theorems. If we have a machine to solve the Langlands program in one day, then we'll think of more things to prove after that. There's a million unsolved questions in number theory unrelated to Langlands, and if we knew Langlands (and why it was true) we could make new conjectures that our theorem proving machine could solve, rather than having to speculate for 50 or 100 years like now.

The possibility he's not considering is that the machine might be better even at conjectures, and then there really is no role for humans once the machine already knows things our primitive meat brains are too small to understand. But what he's saying isn't "pants on head stupid".

I think I’ll take the professional mathematician perception of how AI affects his field over random HN commenter saying it’s “pants on head stupid”

Are humans going to be able to recognize the things AI discovers?

It took us a while to make the planets line up neatly in a heliocentric system. Just last month I read that a whale mother "might" grief while carrying her stillborn child.

The limiting factor is human imagination and comprehension. No offense, but see your comment.

I think AI has already invented new math, but the guys haven't looked for it because they didn't think it possible. And even under their noses, they wouldn't understand what they see.

> It's not what you look at that matters, it's what you see. —Thoreau

This is the dumbest, most troglodyte “solution” to this frontier pushing development. WHO does this benefit besides a handful of mathematicians?

> Under a partnership, the Simons Foundation, Anthropic and OpenAI will commit $15 million in combined funding and resources. The foundation will manage and award funding, including through an open call for proposals, to support workshops and initiatives that help researchers evaluate recent AI-assisted results, learn and use new tools, share perspectives and shape collective standards for AI use.

"Normal technology"?

Lure people? It isn't a cult.